Circuit arrangement providing impedance translation filtering

ABSTRACT

A circuit arrangement for providing impedance translation filtering comprises a first path and a second path. In a base band variant the first path is a feed forward path which comprises first and second series connected transconductance gain stages ( 10, 12 ), and the second path is a feedback which comprises third and fourth transconductance gain stages ( 18, 20 ), each having an inverting output. An output of the first gain stage is coupled to an input of the fourth gain stage. In operation, the impedance presented at its output determines the impedance presented at an input of the circuit arrangement.

The present invention relates to a circuit arrangement providingimpedance translation filtering. An application of the present inventionis effecting high frequency (i.f. or r.f.) filtering in receivers andtransmitters.

Impedance control circuits are known, for example from UK PatentSpecification 2,100,949A, for use in subscriber line interface circuitsin telephone systems. The cited specification discloses an idealisedtransmission system having first and second circuits along which signalspass. A current controlled feedback loop in the first circuit is used tocontrol the impedance of that circuit by a single element so that thecircuit with feedback initiates an idealised circuit having an impedancerepresenting the first circuit. Thus the current—controlled feedbackloop sets the impedance of the circuit. This cited specification doesnot disclose using impedance translation for effecting high frequencyfiltering.

According to a first aspect of the present invention there is provided acircuit arrangement comprising a first path including a first frequencytranslation stage, a second path including a second frequencytranslation stage, an input to the first path being connected to anoutput of the second path, an output of the first path being connectedto an input of the second path, and means for connecting a source oflocal oscillator signals to the first and second frequency translationstages, wherein the frequency of an input signal is translated by thelocal oscillator signals to a lower frequency and wherein the impedanceas viewed from a higher frequency end of the circuit arrangement isdetermined by the impedance presented at a lower frequency end of thecircuit arrangement.

According to a second aspect of the present invention there is provideda circuit arrangement comprising a first path and a second path, thefirst path comprising first and second series connected transconductancegain stages, the second path comprising third and fourthtransconductance gain stages, each having an inverting output, an inputof the third gain stage being coupled to an output of the second gainstage, the output of the fourth gain stage being coupled to an input ofthe first gain stage, and an output of the first gain stage beingcoupled to an input of the fourth gain stage, whereby an impedancepresented at an output of the second gain stage determines the inputimpedance presented at the input of the first gain stage.

According to a third aspect of the present invention there is provided aquadrature receiver comprising input means for connection to a signalsource, input signal dividing means coupled to the input means, thedividing means having first and second outputs, first and second circuitarrangements coupled to the first and second outputs, respectively, thefirst circuit arrangement comprising a first path and a second path, thefirst path comprising a first transconductance mixer having an outputand a first gain stage coupled to the output of the first mixer, and thesecond path comprising a second transconductance gain stage having aninverting output and second transconductance mixer coupled to the outputof the second gain stage, the second mixer having an inverting outputcoupled to an input of the first mixer, an output of the first gainstage being coupled to an input of the second gain stage, the output ofthe second mixer being coupled to an input of the first mixer, and theoutput of the first mixer being coupled to an input of the second mixer,and the second circuit arrangement comprising a first path and a secondpath, the first path comprising a third transconductance mixer having anoutput and a third gain stage coupled to the output of the third mixer,the second path comprising a fourth transconductance gain stage havingan inverting output and a fourth transconductance mixer coupled to theoutput of the fourth gain stage, the fourth mixer having an invertingoutput coupled to an input of the third mixer, an output of the thirdgain stage being coupled to an input of the fourth gain stage, theoutput of the fourth mixer being coupled to an input of the third mixer,and the output of the third mixer being coupled to an input of thefourth mixer, and a local oscillator signal source having first andsecond quadrature related outputs, the first output being coupled to thefirst and second mixers and the second output being coupled to the thirdand fourth mixers.

According to a fourth aspect of the present invention there is provideda transmitter comprising first and second means for connection torespective first and second signal sources, first and second circuitarrangements coupled to the respective means for connection to the firstand second signal sources, the first circuit arrangement comprising afirst path and a second path, the first path comprising a firsttransconductance gain stage having an inverting output and a firsttransconductance mixer coupled to the output of the first gain stage,the first mixer having an inverting output, the second path comprising asecond transconductance mixer having an output and a second gain stagecoupled to the output of the second mixer, the output of the secondmixer being coupled to an input of the first mixer, an output of thesecond gain stage being coupled to an input of the first gain stage, theoutput of the first mixer being coupled to an input of the second mixerand to a signal combining means, and the second circuit arrangementcomprising a first path and a second path, the first path comprising athird transconductance gain stage having an inverting output and a thirdtransconductance mixer coupled to the output of the third gain stage,the third mixer having an inverting output, the second path comprising afourth transconductance mixer having an output and fourthtransconductance gain stage coupled to the output of the fourth mixer,the output of the fourth mixer being coupled to an input of the thirdmixer, an output of the fourth gain stage being coupled to an input ofthe third gain stage, and the output of the third mixer being coupled toan input of the fourth mixer and to the signal combining means.

Combining the ability to be able to use the impedance presented at theoutput of a circuit arrangement to determine its input impedance withpairs of quadrature mixers performing down- and up-mixing allows a wellcontrolled impedance variation at base band to also produce an impedancevariation and thereby a filtering effect at high (i.f. or r.f.)frequencies. The effective r.f. filtering may then be used withadvantage in transceiver architectures, for example to avoid external,off-chip components, or to relax performance requirements.

The present invention will now be described, by way of example, withreference to the accompanying drawings, wherein

FIG. 1 is a block schematic diagram of a baseband model of the circuitarrangement in accordance with the present invention,

FIG. 2 is a block schematic diagram of an ideal baseband quadraturemodel of the circuit arrangement made in accordance with the presentinvention,

FIG. 3 is a block schematic diagram of a quadrature frequency—shiftingmodel,

FIG. 4 is a version of FIG. 3 showing impedance translation,

FIG. 5 is a block schematic diagram of a quadrature receiver,

FIG. 6 is a block schematic diagram of a quadrature transmitter, and

FIG. 7 is a block schematic of a reciprocal impedance translation stage.

In the drawings the same reference numerals have been used to indicatecorresponding features.

Referring to FIG. 1, the basic circuit block is shown within the brokenlines and comprises a first, feed forward path comprising first andsecond series connected transconductance amplifiers 10, 12 having gainsof G₁ and G₂, respectively. A second, feedback path is connected betweenthe output 14 of the basic circuit block and the input 16 to the basiccircuit block. The second path comprises a third and fourth seriesconnected transconductance amplifiers 18, 20 having negative gainsG₂′,G₁′ and inverting outputs. The output of the first amplifier 10 andthe input of the fourth amplifier 20 are interconnected by a conductivelink 21. The first to fourth amplifiers 10, 12, 18 and 20 may bedifferential amplifiers and the inverted outputs of the third and fourthamplifiers 18, 20 may be obtained by swapping over their outputs. Theinput impedance to the second amplifier 12 is represented by a resistorz₁ but is more likely to be implemented as an RC filter. The impedancevalue of z₁ is preferably high. The transconductance amplifiers give anoutput current proportional to the input voltage. As will bedemonstrated by the following mathematical analysis, the impedance z_(s)seen at the input 16 of the circuit arrangement is determined by theimpedance z₂ presented at the output 14 of the circuit block.

For convenience of reference, a source voltage V_(s) is shown connectedby the input impedance z_(s) to an input 16. A voltage V₀ at the inputof the amplifier 10 is amplified and represented by a current l₀′ on itsoutput. A voltage V₁ at the input of the amplifier 12 is amplified andrepresented by a current l₂″. A current l₂ flows into the impedance z₂and produces a voltage V₂. The voltage V₂ on the input of the amplifier18 is transconducted to a current l₂′. Lastly a voltage V₁ on the inputof the amplifier 20 is transconducted to a current l₀″.

Starting with the conditions at the centre

V ₁=(I ₀ ′+I ₂′(z ₁   (1)

Now

I ₀ ′=G ₁ V ₀

and

I ₂ ′=G ₂ V ₂

so

I ₀ ′+I ₂ ′=G ₁ V ₀ +G ₂ ′V ₂

giving

V ₁=(G ₁ V ₀ +G ₂ ′V ₂)z ₁   (2)

This gives the output current as:

I ₂ =G ₂ V ₁

Substituting (2) for V₁ gives:

I ₂=(G ₁ G ₂ V ₀ +G ₂ G ₂ ′V ₂)z ₁   (3)

and the current drawn at the input as:

I ₀ =−G ₁ ′V ₁

Substituting (2) for V₁ gives:

I ₀=(−G ₁ G ₁ ′V ₀ −G ₁ ′G ₂ V ₂)z ₁   (4)

These two equations define the currents at output and input as afunction of the voltages at the output and input.

Now the current at the output is determined by the load impedancepresent

V ₂ =I ₂ z ₂   (5)

so using this relationship then gives for the output current from eqn.(3) gives

 I ₂ =G ₁ G ₂ V ₀ z ₁ +G ₂ G ₂ ′I ₂ z ₁ z ₂

$\begin{matrix}\begin{matrix}{I_{2} = {{G_{1}\quad G_{2}\quad V_{0}z_{1}} + {G_{2}\quad G_{2}^{\prime}\quad I_{2}\quad z_{1}\quad z_{2}}}} \\{ \Rightarrow{I_{2}\quad ( {1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} )}  = {G_{1}\quad G_{2}\quad V_{0}z_{1}}} \\{ \Rightarrow I_{2}  = {V_{0}\{ \frac{G_{1}\quad G_{2}\quad z_{1}}{1 - {G_{2}G_{2}^{\prime}\quad z_{1}\quad z_{2}}} \}}}\end{matrix} & (6)\end{matrix}$

and for the input current from eqn. (4)

I ₀ =−G ₁ G ₁ ′V ₀ z ₁ −G ₁ ′I ₂ z ₁ z ₂

using (6) then $\begin{matrix}{I_{0} = { {{{- G_{1}}\quad G_{1}^{\prime}\quad V_{0}\quad z_{1}} - {\frac{G_{1}^{\prime}\quad G_{2}^{\prime}\quad z_{1}\quad {z_{2} \cdot G_{1}}\quad G_{2}\quad z_{1}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}}\quad V_{0}}}\Rightarrow I_{0}  = { {V_{0}\{ \frac{{{- G_{1}}\quad G_{1}^{\prime}\quad z_{1}} + {G_{1}\quad G_{1}^{\prime}\quad {z_{1} \cdot G_{2}}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}} - {G_{1}^{\prime}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}\quad G_{1}\quad G_{2}\quad z_{1}}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} \}}\Rightarrow I_{0}  = {V_{0}\{ \frac{{- G_{1}}\quad G_{1}^{\prime}\quad z_{1}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} \}}}}} & (7)\end{matrix}$

Given the load impedance, this then has defined the currents flowing inthe output and input circuits. The minus sign in expression (7) isexplained by the definitions of the current flow, and the expectationthat G₁ is negative.

Having derived the current at the input the input impedance, z_(in)presented by the block can be calculated, which is simply$\begin{matrix}{z_{in} = {\frac{V_{0}}{I_{0}} = \frac{{G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}} - 1}{G_{1}\quad G_{1}^{\prime}\quad z_{1}}}} & (8)\end{matrix}$

To see how the circuit behaves when the feedback loop gain is high, if|G₂G₂′z₁z₂|>>1

then $\begin{matrix} {z_{in} \approx \frac{G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}{G_{1}\quad G_{1}^{\prime}\quad z_{1}}}\Rightarrow{z_{in} \approx {\frac{G_{2}\quad G_{2}^{\prime}}{G_{1}\quad G_{1}^{\prime}} \cdot z_{2}}}  & (9)\end{matrix}$

The important property of the circuitry block is thus demonstrated, thatthe impedance at the input is related to (and usually proportional to)the impedance present at its output.

In the meantime however, to complete the description, the signal voltageat the output is simply obtained by the output current flowing in theload impedance

Eqn.(6) in Eqn. (5) $\begin{matrix}{V_{2} = {\frac{G_{1}\quad G_{2}\quad z_{1}\quad z_{2}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} \cdot V_{0}}} & (10)\end{matrix}$

The expression makes sense, as it is the forward gain multiplied by theclosed loop response (1—loop gain)⁻¹ for the feedback loop formed by theoutput and internal circuit. The loop formed around the input circuitnaturally does not have an influence, for a given voltage input V₀.Again, to see how the circuit behaves when the feedback loop gain ishigh, if |G₂G₂′z₁z₂|>>1 then the voltage gain (10) simplifies to$\begin{matrix}{V_{2} \approx {\frac{- G_{1}}{G_{2}^{\prime}}\quad V_{0}}} & (11)\end{matrix}$

Intuitively this is the forward gain G₁z₁ followed by the feedback G₂′z,with the internal impedance z₁ dropping out of the expression, and theminus signal explainable by G₂′ being negative.

The current gain, the ratio of the currents flowing in the output andthe input is also of interest

Eqns. (6) and (7) $\begin{matrix}{\frac{I_{2}}{I_{0}} = {\frac{G_{1}\quad G_{2}\quad z_{1}}{{- G_{1}}\quad G_{1}^{\prime}\quad z_{1}} = \frac{G_{2}}{G_{1}^{\prime}}}} & (12)\end{matrix}$

which is as it should be, since the voltage V₁ is common input to bothtransconductor amplifiers 12, 20, so the ratio of the currents is thatof the gains. The minus sign reflects the fact that the currents aredefined in FIG. 1 flowing in opposite directions, so G₁′ is negative.The result is also consistent with the impedance relationship (9) andthe voltage scaling between input and output (11).

Now the application of the circuit block together with source circuit,with the voltage source V_(s) and source impedance z_(s) will beexamined. The voltage at the input of the block is then determined bythe voltage dropped due to the current flow in the source impedance:

 V ₀ =V _(s) −I ₀ z _(s)   (13)

substituting in the current flow result (7) we have $\begin{matrix}{V_{0} = { {V_{s} - {V_{0}\{ \frac{{- G_{1}}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} \}}}\Rightarrow{V_{0}\{ {1 - \frac{G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}}} \}}  = { V_{s}\Rightarrow V_{0}  = {V_{s}\{ \frac{1}{1 - \frac{G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}}} \}}}}} & (14)\end{matrix}$

This makes sense as there are two, nested feedback loops, the first onewith loop gain G₁G₁′z₁z_(s) having its loop gain modified by the secondloop with loop gain G₂G₂′z₁z₂.

Further rearrangement of (14) then gives the more manageable expression$\begin{matrix}{V_{0} = {V_{s}\{ \frac{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}} - {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}} \}}} & (15)\end{matrix}$

It is important to note the basic effect, that the voltage developed atthe input to the circuit block is being determined, as a result of thefeedback, by the impedance z₂ presented at its output. This means thatif a filter which presents a frequency—dependent input impedance ispresent at the output, then its effect will also be felt at the input ofthe circuit block.

If there is strong feedback, |G₂G₂′z₁z₂|>>1 then $\begin{matrix}{V_{0} \approx {V_{s}\{ \frac{G_{2}\quad G_{2}^{\prime}\quad z_{2}}{{G_{2}\quad G_{2}^{\prime}\quad z_{2}} + {G_{1}\quad G_{1}^{\prime}\quad z_{s}}} \}}} & (16)\end{matrix}$

Note again that the internal impedance z₁ has dropped out of theexpression; it determines the internal impedance level and the feedbackloop gains, only indirectly influence the transfer function betweeninput and output. If |G₁G₁′z_(s)|>>|G₂G₂′z₂| as will be the case forexample if z₂ is small, for an out-of-band signal, then $\begin{matrix}{V_{0} \approx {V_{s}\quad \frac{G_{2}\quad G_{2}^{\prime}\quad z_{2}}{G_{1}\quad G_{1}^{\prime}\quad z_{s}}}} & (17)\end{matrix}$

so that if G₁, G₁′, G₂, G₂′, z_(s) are substantially independent offrequency, then

V ₀ ∝z ₂ ·V _(s)   (18)

and the signal level at the input of the block is simply proportional tothe load impedance at the baseband output of the block, z₂.

Turning now to the signal level at the output, combining equations (10)and (14) gives $\begin{matrix}{V_{2} = { {V_{s}\quad {\frac{G_{1}\quad G_{2}\quad z_{1}\quad z_{2}}{( {1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} )} \cdot \frac{1}{( {1 - ( \frac{G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}}} )} )}}}\Rightarrow V_{2}  = {V_{s}\quad \frac{G_{1}\quad G_{2}\quad z_{1}\quad z_{2}}{( {1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}} - {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{2}}} )}}}} & (19)\end{matrix}$

So the forward gain voltage gain of each stage, being thetransconductance multiplied by the load impedances, is modified by thefeedback loop gains.

If there is strong feedback, |G₁G₁′z₁z₂|>>1 or |G₂G₂′z₁z₂|>>1 then$\begin{matrix}{ {V_{2} \approx {{- V_{s}}\quad \frac{G_{1}\quad G_{2}\quad z_{1}\quad z_{2}}{{G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad z_{2}} + {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad z_{s}}}}}\Rightarrow{V_{2} \approx {{- V_{s}}\quad \frac{G_{1}\quad G_{2}\quad z_{2}}{{G_{1}\quad G_{1}^{\prime}\quad z_{s}} + {G_{2}\quad G_{2}^{\prime}\quad z_{2}}}\quad {or}}} {V_{2} \approx {{- V_{s}}\quad {\frac{G_{1}}{G_{2}^{\prime}} \cdot \frac{z_{2}}{{\frac{G_{1}\quad G_{1}^{\prime}}{G_{2}\quad G_{2}^{\prime}}\quad z_{s}} + z_{2}}}}}} & (20)\end{matrix}$

which is consistent with the impedance scaling result, as can be seen byreformulating as$V_{2} \approx {{- V_{s}}\quad {\frac{G_{1}}{G_{2}^{\prime}} \cdot \frac{\frac{G_{2}\quad G_{2}^{\prime}}{G_{1}G_{1}^{\prime}}\quad z_{2}}{z_{2} + {\frac{G_{2}\quad G_{2}^{\prime}}{G_{1}\quad G_{1}^{\prime}}\quad z_{2}}}}}$

and then using (9) to re-express in terms of the input impedance z_(in)presented is by the block, giving $\begin{matrix}{V_{2} \approx {{- V_{s}}\quad {\frac{G_{1}}{G_{2}^{\prime}} \cdot \frac{z_{in}}{z_{s} + z_{in}}}}} & (21)\end{matrix}$

This is a satisfying result; a potential divider is being formed byz_(in) and z_(s), with the voltage then being amplified to the outputwith gain −G₁/G₂′ as per equation (11).

Remember that G₂′ is negative.

If as can be the case for an out-of-band signal the impedance${{z_{2}}{\operatorname{<<}}G_{1}\quad \frac{G_{1}^{\prime}}{G_{2}\quad G_{2}^{\prime}}\quad z_{s}}$

then (20) can be further simplified to $\begin{matrix}{V_{2} \approx {{- V_{s}}\quad {\frac{G_{2}}{G_{1}^{\prime}} \cdot \frac{z_{2}}{z_{s}}}}} & (22)\end{matrix}$

and if G₁, G₁′, G₂, G₂′, z_(s) are all independent of frequency then

V ₂ ∝z ₂ ·V _(s)

The signs all appear to be correct if as expected the signs of G₁′ andG₂′ are negative.

This also ensures stability of the feedback loops, $\frac{1}{1 - \beta}$

where β should be negative.

The performance can be improved by making l₀′=l₂′ more closely, that isby increasing z₁ directly or indirectly via buffering circuitry betweenthe current summing junction and the drive to the transconductoramplifiers.

Referring to FIG. 2 which shows an ideal quadrature model. ComparingFIGS. 1 and 2 it is evident that the in-phase I and quadrature phase Qcircuits are of identical layout with the exceptions that the referencenumbers of the transconductance amplifiers has “I” and “Q” added and thesubscripts “i” and “q” have been used in the referencing of the variousvoltages and currents. In the interests of brevity a detaileddescription will not be given of FIG. 2 as the description of therespective I and Q circuits has been amply covered with reference toFIG. 1.

FIG. 3 is a variant of FIG. 2 in which the transconductance ammplifiers101, 201, 10 Q and 20 Q have been replaced by transconductance mixers221, 241, 22 Q and 24 Q, respectively. The mixers 221 and 22 Q havedouble the gain of the mixers 241 and 24 Q. Also the mixers 241 and 24 Qhave inverting outputs.

A signal source 26 is coupled by way of a signal splitter 28 to theinputs 161 and 16 Q of the respective circuit blocks. Quadrature relatedlocal oscillator signals are supplied to the mixers 221, 241 and 22 Q,24 Q, respectively.

In order to explain the operation of FIG. 3 in general terms it will beassumed for simplicity that the gains paths are identical and that thereis a perfect 90° phase shift between them. There is a frequency downconversion in the mixer 221 or 22 Q and a frequency up conversion in themixer 241 or 24 Q. Accordingly it is necessary to consider the effectsof both frequency translations in the following mathematical analysis.

In the case of frequency translation down by (−f^(osc)):

Input voltage to mixer 221,

V ₀−α₀ sin(2πft−φ ₀)   (23)

$I_{0i}^{\prime} = {\frac{2G_{1}\quad a_{0}}{2}\quad \{ {{\sin \quad ( {{2\quad \pi \quad ( {f - f_{osc}} )\quad t} - \varphi_{0}} )} + {\sin \quad ( {{2\quad \pi \quad ( {f + f_{osc}} )\quad t} - \theta_{0}} )}} \}}$

The double frequency term is removed by filtering, leaving

I _(0i) ′=G ₁α₀ sin(2π(f−f _(osc))t−φ ₀)   (24)

and similarly$I_{0q}^{\prime} = {\frac{2G_{1}a_{0}}{2}\{ {{\cos ( {{2\quad {\pi ( {f - f_{osc}} )}\quad t} - \varphi_{0}} )} - {\cos ( {{2\quad \pi \quad ( {f + f_{osc}} )\quad t} - \theta_{0}} )}} \}}$

which with the double frequency removed gives

I _(0q) ′G ₁α₀ cos(2π(f−f _(osc))t−φ ₀)   (25)

that is for each I and Q path a gain of G₁ and a frequency translationdown by (−f_(osc))

In the case of frequency translation up by (+f_(osc)):

Input voltage to mixer 241,

V _(1i)=α₁ sin(2π(f−f _(osc))t−φ ₁)   (26)

Input voltage to mixer 24 Q,

V _(lq)=α₁ cos(2π)f−f _(osc))t−φ ₁)   (27)

then

I ₀ ″=V _(1i) G ₁′cos(2πf _(osc) t)+V _(1q) G ₁′sin(2πf _(osc) t)

so by standard trigonometry

 I ₀ ″G ₁′α₁{sin(2π(f−f _(osc))t−φ ₁)cos(2πf _(osc) t)+cos(2π(f−f_(osc))t−φ _(t))sin(2πf _(osc) t)}

I ₀ ″G ₁′α₁ sin(2π(f−f _(osc))f−φ ₁+2πf _(osc) t)

I ₀ ″G ₁ ′α ₁ sin(2πft−φ ₁)  (28)

that is, a gain of G₁′ and a frequency translation up by (+f_(osc))takes place.

Putting the two parts together to build an impedance couplingarrangement including a frequency translation as in FIG. 3. First we setup an input signal:

V _(s)=α_(s) sin(2πf _(s) t−φ_(s))   (29)

and make z_(s),z₁,z₂ each a function of frequency; z_(s)(f),z₁(f),z₂(f)then from (15) $\begin{matrix}{V_{0} = {a_{s}\sin \quad ( {{2\quad \pi \quad f_{s}t} - \varphi_{s}} )\quad {\{ \frac{1 - {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}}}{1 - \quad {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}} - \quad {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{s}( f_{s} )}}} \}}}} & (30)\end{matrix}$

where the voltage V₀ appearing at the block input is the input signal,subjected to the input impedance applying at f_(s) and the basebandimpedances applying at the frequency of the mixed down signal, at(f_(s)−f_(osc))

The approximations used above still apply, so if there is strongfeedback, |G₂G₂′z₁(f_(s)−f_(osc))z₂(f_(s)−f_(osc))|>>1, then$\begin{matrix}{V_{0} \approx {a_{s}\sin \quad ( {{2\quad \pi \quad f_{s}t} - \varphi_{s}} )\{ \frac{{G_{2}\quad G_{2}^{\prime}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}\quad}{{G_{2}\quad G_{2}^{\prime}\quad z_{2}\quad ( {f_{s} - f_{osc}} )} + {G_{1}\quad G_{1}^{\prime}{z_{s}( f_{s} )}}} \}}} & (31)\end{matrix}$

and if the loop gain around the source circuit is greater than thataround the load circuit, |G₁G₁′z_(s)(f_(s))|>>|G₂G₂′z₂(f_(s)−f_(osc))|$\begin{matrix}{V_{0} \approx {a_{s}\sin \quad {( {{2\quad \pi \quad f_{s}t} - \varphi_{s}} ) \cdot \frac{G_{2}G_{2}^{\prime}}{G_{1}\quad G_{1}^{\prime}} \cdot \frac{z_{2}\quad ( {f_{s} - f_{osc}} )}{z_{s}( f_{s} )}}}} & (32)\end{matrix}$

Now looking at the output voltage, from (19), and bearing in mind (24),a signal is produced that is frequency shifted, and subject to the loopgain and impedance effects.

For the I channel: $\begin{matrix}{V_{2i} = {a_{s}{{\sin \quad( {{2\quad {\pi ( {f_{s} - f_{osc}} )}t}\quad - \varphi_{s}} )} \cdot {\frac{( {G_{1}\quad G_{2}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}} )}{( {1 - \quad {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}} - \quad {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{s}( f_{s} )}}}\quad )}}}}} & (33)\end{matrix}$

and if there is strong feedback, either

|G ₁ G ₁ ′z ₁(f _(s) −f _(osc))z _(s)(f _(s))|>>1 or |G ₂ G ₂ ′z ₁(f_(s) −f _(osc))z ₂(f _(s) −f _(osc))|>>1,

then as in equation (20) this reduces to $\begin{matrix}{V_{2i} \approx {{- a_{s}}\sin \quad {( {{2\quad {\pi ( {f_{s} - f_{osc}} )}t}\quad - \varphi_{s}} ) \cdot {\frac{G_{1}\quad G_{2}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}{{\quad {{G_{1}\quad G_{1}^{\prime}{z_{s}( f_{s} )}} + {G_{2}\quad G_{2}^{\prime}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}}}\quad}}}}} & (34)\end{matrix}$

The minus sign is due to G₁′ and G₂′ being negative. Similarly for the Qchannel: $\begin{matrix}{V_{2q} = {a_{s}{{\cos \quad( {{2\quad {\pi ( {f_{s} - f_{osc}} )}t}\quad - \varphi_{s}} )} \cdot {\frac{( {G_{1}\quad G_{2}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}} )}{( {1 - \quad {G_{2}\quad G_{2}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{2}( {f_{s} - f_{osc}} )}} - \quad {G_{1}\quad G_{1}^{\prime}\quad z_{1}\quad ( {f_{s} - f_{osc}} )\quad {z_{s}( f_{s} )}}}\quad )}}}}} & (35)\end{matrix}$

and if there is strong feedback

|G ₁ G ₁ ′z ₁(f _(s) −f _(osc))z _(s)(f _(s))|>>1 or |G ₂ G ₂ ′z ₁(f_(s) −f _(osc))z ₂(f _(s) −f _(osc))|>>1,

then $\begin{matrix}{V_{2q} \approx {{- a_{s}}\cos \quad {( {{2\quad {\pi ( {f_{s} - f_{osc}} )}t}\quad - \varphi_{s}} ) \cdot {\frac{G_{1}\quad G_{2}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}{{\quad {{G_{1}G_{1}^{\prime}{z_{s}( f_{s} )}} + {G_{2}\quad G_{2}^{\prime}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}}}\quad}}}}} & (36)\end{matrix}$

So from an input signal, frequency f_(s) and amplitude a_(s) aquadrature pair of signals are produced at the output, with a frequencyof (f_(s)−f_(osc)) and an amplitude a₂ of approximately$a_{s} \cdot {\frac{G_{1}\quad G_{2}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}{{\quad {{G_{1}G_{1}^{\prime}{z_{s}( f_{s} )}} + {G_{2}\quad G_{2}^{\prime}\quad z_{2}\quad ( {f_{s} - f_{osc}} )}}}\quad}.}$

The gain is thus determined by the impedances experienced in thebaseband part of the circuitry, together with the source impedance seenat the r.f. input.

Furthermore, as demonstrated by equations (30) to (32) the signal levelat the input to the block is modified by the effect of the basebandimpedance z₂ (f_(s)−f_(osc)). Therefore narrow-band filter effects canbe produced, without the need to implement high quality tuned circuitsat high frequencies.

The above approximate expression for the amplitude a₂ can meaningfullybe further rearranged to give a gain of $\begin{matrix}{\frac{a_{2}}{a_{s}} = {\frac{G_{1}}{G_{2}^{\prime}} \cdot \frac{z_{2}\quad ( {f_{s} - f_{osc}} )}{{\quad {{\frac{G_{1}G_{1}^{\prime}}{G_{2}\quad G_{2}^{\prime}}{z_{s}( f_{s} )}} + {z_{2}\quad ( {f_{s} - f_{osc}} )}}}\quad}}} & (37)\end{matrix}$

The gain between r.f. input and baseband output is then the ratio of thegains acting on the internal common point, G₁/G₂′, modified by theimpedance across which the signal is developed, the baseband loadimpedance, z₂(f_(s)−f_(osc)), fed by the r.f. source impedance scaled bythe gain ratios and translated to be effective at the baseband output,$\frac{G_{1}G_{1}^{\prime}}{G_{2}\quad G_{2}^{\prime}}{{z_{s}( f_{s} )}.}$

For the sake of completeness, FIG. 4 shows an impedance translationrepresentation of FIG. 3. The references z_(rf) and z_(bb) respectivelymean the radio frequency impedance and the base band impedance. Theremainder of the references have the same meaning as used in FIG. 3.

FIG. 5 illustrates a radio receiver which is based on the frequencyshifting model shown in FIGS. 3 and 4. The signal source in the case ofthe receiver is an antenna 30 which is coupled to the signal splitter28. However the signal source could be an i.f. signal derived from theoutput of a r.f. front end. The outputs from the respective I and Qcircuit blocks are applied to low pass filters 32, 34 which select thewanted products from the frequency translation. A local oscillator 36 isshown connected to a phase shifter 38 which quadrature related localoscillator signals cos(ω_(osc)t) and sin(ω_(osc)t) to the mixers 221,241 and 22 Q, 24 Q, respectively. The frequency translation andfiltering by the circuit blocks has already been described above and inthe interests of brevity will not be repeated again.

FIG. 6 illustrates a transmitter which is based on the frequencyshifting model shown in FIGS. 3 and 4. In operation, quadrature relatedmodulating signals V_(i), V_(q) represented by the signal sources 40, 42are applied to the circuit blocks I and Q by way of low pass filters 32,34. The signals are frequency up-converted in the mixers 241, 24 Q andsupplied to a signal combiner 44, which is a reciprocal of a signalsplitter, the output of which is coupled to the antenna 30. The signalsfrom the mixers 241, 24 Q are frequency down converted in the mixers221, 22 Q, respectively.

The oscillator 36 and the phase splitter 38 provide the oscillatorsignals for up and down conversion, as appropriate.

The mathematical analysis provided above for the frequency shiftingmodel is valid for the transmitter.

FIG. 7 is a simplification of the impedance translation arrangementshown in FIG. 4. The simplification comprises omitting thetransconductance amplifiers 121, 12 Q, 181, 18 Q, the conductive links21 and the impedances zi. In this simplified arrangement the impedanceseen looking into one side of the circuit block is (proportional to) thereciprocal of the impedance z₂ present at the output of the other side.

In a practical application of the circuit block the impedance z₂presents a high impedance for out-of-band baseband signals. When theimpedance is reciprocally translated to r.f., the impedance looking intothe circuit block is then low for such signals, reducing their amplitudethereby facilitating the filtering of these signals.

In the present specification and claims the word “a” or “an” precedingan element does not exclude the presence of a plurality of suchelements. Further, the word “comprising” does not exclude the presenceof other elements or steps than those listed.

From reading the present disclosure, other modifications will beapparent to persons skilled in the art. Such modifications may involveother features which are already known in the design, manufacture anduse of transmitters and receivers and components therefor and which maybe used instead of or in addition to features already described herein.

What is claimed is:
 1. A circuit arrangement comprising a first pathincluding a first fequency translation stage, a second path including asecond frequency translation stage, an input to the first path beingconnected to an output of the second path, an output of the first pathbeing connected to an input of the second path, and means for connectinga source of local oscillator signals to the first and second frequencytranslation stages, wherein the frequency of an input signal istranslated by the local oscillator signals to a lower frequency andwherein the impedance as viewed from a higher frequency end of thecircuit arrangement is determined by the impedance presented at a lowerfrequency end of the circuit arrangement.
 2. A circuit arrangement asclaimed in claim 1, characterised in that the determined impedancerelationship is a reciprocal one.
 3. A circuit arrangement comprising afirst path and a second path, the first path comprising first and secondseries connected transconductance gain stages, the second pathcomprising third and fourth transconductance gain stages, each having aninverting output, an input of the third gain stage being coupled to anoutput of the second gain stage, the output of the fourth gain stagebeing coupled to an input of the first gain stage, and an output of thefirst gain stage being coupled to an input of the fourth gain stage,whereby an impedance presented at an output of the second gain stagedetermines the input impedance presented at the input of the first gainstage.
 4. A circuit arrangement as claimed in claim 3, characterised inthat an impedance device is coupled to an input of the second gainstage.
 5. A circuit arrangement as claimed in claim 3, characterised inthat the third and fourth gain stages have negative gains.
 6. A circuitarrangement as claimed in claim 3, characterised in that the first gainstage comprises a first transconductance mixer and the fourth gain stagecomprises a second transconductance mixer having an inverting output,and in that a source of local oscillator signals is coupled inputs ofthe first and second mixers.
 7. A quadrature receiver comprising inputmeans for connection to a signal source, input signal dividing meanscoupled to the input means, the dividing means having first and secondoutputs, first and second circuit arrangements coupled to the first andsecond outputs, respectively, the first circuit arrangement comprising afirst path and a second path, the first path comprising a firsttransconductance mixer having an output and a first gain stage coupledto the output of the first mixer, and the second path comprising asecond transconductance gain stage having an inverting output and asecond transconductance mixer coupled to the output of the second gainstage, the second mixer having an inverting output coupled to an inputof the first mixer, an output of the first gain stage being coupled toan input of the second gain stage, the output of the second mixer beingcoupled to an input of the first mixer, and the output of the firstmixer being coupled to an input of the second mixer, and the secondcircuit arrangement comprising a first path and a second path, the firstpath comprising a third transconductance mixer having an output and athird gain stage coupled to the output of the third mixer, the secondpath comprising a fourth transconductance gain stage having an invertingoutput and a fourth transconductance mixer coupled to the output of thefourth gain stage, the fourth mixer having an inverting output coupledto an input of the third mixer, an output of the third gain stage beingcoupled to an input of the fourth gain stage, the output of the fourthmixer being coupled to an input of the third mixer, and the output ofthe third mixer being coupled to an input of the fourth mixer, and alocal oscillator signal source having first and second quadraturerelated outputs, the first output being coupled to the first and secondmixers and the second output being coupled to the third and fourthmixers.
 8. A receiver as claimed in claim 7, characterised in that afirst impedance device is coupled to an input of the first gain stageand in that a second impedance device is coupled to the input of thethird gain stage.
 9. A transmitter comprising first and second means forconnection to respective first and second signal sources, first andsecond circuit arrangements coupled to the respective means forconnection to the first and second signal sources, the first circuitarrangement comprising a first path and a second path, the first pathcomprising a first transconductance gain stage having an invertingoutput and a first transconductance mixer coupled to the output of thefirst gain stage, the first mixer having an inverting output, the secondpath comprising a second transconductance mixer having an output and asecond gain stage coupled to the output of the second mixer, the outputof the second mixer being coupled to an input of the first mixer, anoutput of the second gain stage being coupled to an input of the firstgain stage, the output of the first mixer being coupled to an input ofthe second mixer and to a signal combining means, and the second circuitarrangement comprising a first path and a second path, the first pathcomprising a third transconductance gain stage having an invertingoutput and a third transconductance mixer coupled to the output of thethird gain stage, the third mixer having an inverting output, the secondpath comprising a fourth transconductance mixer having an output andfourth transconductance gain stage coupled to the output of the fourthmixer, the output of the fourth mixer being coupled to an input of thethird mixer, an output of the fourth gain stage being coupled to aninput of the third gain stage, and the output of the third mixer beingcoupled to an input of the fourth mixer and to the signal combiningmeans.
 10. An integrated circuit comprising the circuit arrangement asclaimed in claim 1.